diff --git a/Misc/NEWS b/Misc/NEWS
index 24018acf4a6..dcc2b81e8d3 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -56,6 +56,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #6271: mmap tried to close invalid file handle (-1) when annonymous.
+  (On Unix)
+
 - Issue #6258: Support AMD64 in bdist_msi.
 
 - Issue #5262: Fixed bug in next rollover time computation in
diff --git a/Modules/mmapmodule.c b/Modules/mmapmodule.c
index cbacc2fc252..1d0f490d5ab 100644
--- a/Modules/mmapmodule.c
+++ b/Modules/mmapmodule.c
@@ -158,7 +158,8 @@ mmap_close_method(mmap_object *self, PyObject *unused)
 #endif /* MS_WINDOWS */
 
 #ifdef UNIX
-	(void) close(self->fd);
+	if (0 <= self->fd)
+		(void) close(self->fd);
 	self->fd = -1;
 	if (self->data != NULL) {
 		munmap(self->data, self->size);